Dynamic programming solves interval ordering in O(2^n poly(n)) time via oracle access to f, in polynomial time when f-f(0) is subadditive or superadditive, with a 2^{n-1} lower bound and NP-hardness for some simple f.
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Computational Complexity of the Interval Ordering Problem
Dynamic programming solves interval ordering in O(2^n poly(n)) time via oracle access to f, in polynomial time when f-f(0) is subadditive or superadditive, with a 2^{n-1} lower bound and NP-hardness for some simple f.